Masks for optical lithography and other patterns having features in the nanometer regime are typically fabricated using beam lithography processes, such as electron beam writing or laser beam writing. In a beam lithography process, a radiation sensitive resist on a substrate is exposed by beam writing. The resist is then developed to remove the exposed (in the case of a positive tone resist) or unexposed (in the case of a negative tone resist) resist portions. The resist portions that remain are used as a basis for a pattern transfer on the substrate. This pattern transfer includes, in a mask fabrication example, etching a masking layer on a transparent mask blank in the removed resist areas.
The energy deposited by beam writing in the resist (i.e., the exposure dose) has an influence on the development process. This means—in the exemplary case of a positive tone resist—that below a predefined energy threshold (that is required to fully expose the resist), the resist cannot be removed by development. When the same feature such as an isolated line having a certain nominal line width (as written by a beam writing apparatus) is exposed with different exposure doses at or above the energy threshold, the actual line width after resist development (and, optionally, after a pattern transfer process) increases with the exposure dose as shown in FIG. 1 for an isolated line and assuming a nominal line width of 0.30 μm.
In FIG. 1, the x axis is indicative of the exposure dose and the y axis is indicative of the actual Critical Dimension, or CD. The actual CD is the measured CD after resist exposure, resist development and, optionally, pattern transfer. The pattern transfer is needed in case the measurements are not performed on the developed resist pattern but on a pattern transferred (e.g., etched) through the patterned resist into a layer below the resist layer. In the present exemplary case of a line, the CD corresponds to the line width.
There are various reasons for the dependency of the CD on the exposure dose. These reasons include the beam profile, artefacts introduced by the beam writing apparatus (e.g., beam blur and focus errors), physical effects of beam writing (e.g., electron scattering and fogging) and process artefacts (e.g., resist blur, process loading effects of one or both of development and etching, and pattern transfer effects).
Electron scattering artefacts have been widely investigated in electron beam lithography. When a resist has been exposed by electron beam writing, electron scattering prevents that the developed resist regions mirror exactly the exposed resist regions. Electron scattering occurs within the resist itself as well as at the underlying substrate (in terms of backscattering). Moreover, some of the scattered electrons escape the resist towards the beam writing apparatus and are reflected back by an objective lens of the apparatus. This effect is called fogging. Correction of backscattering and fogging as well as proximity effect correction for dense patterns are widely employed today to compensate electron scattering artefacts.
One of the challenges in a beam lithography process is the search for an optimal process point. The process point can be defined, inter alia, in terms of a so-called process dose. The optimum process dose for a given beam lithography process is dependent on the overall process parameters, such as resist sensitivity, resist thickness, development parameters (e.g., chemistry, time and temperature of the development process), etching bias and loading, and so on.
In some cases, the optimum process dose is the so-called base dose that is set at the beam writing apparatus and calibrated using experimental data. By additionally applying a dose factor to the base dose for dose modulation, a proximity effect correction of electron scattering artefacts and similar artefacts that have a dependency on a feature density of the target pattern can separately be applied. The actual exposure dose will in such a scenario be jointly determined by the base dose and the dose factor.
In regard of the dependency of the actual CD, such as a line width after resist development, on the exposure dose, one could for example set the exposure dose to the so-called dose-to-size. So when an actual CD of 0.30 μm is desired, the dose-to-size in the scenario of FIG. 1 is 120 ρC/cm2.
However, an actual CD of 0.30 μm could also be obtained by using a higher (or lower) exposure dose if the nominal CD as written by the beam writing apparatus was shrank (or expanded). As exemplarily illustrated in FIG. 2, an exposure dose of 140 μC/cm2 (i.e., an exposure dose higher than the dose-to-size of 120 μC/cm2) results in CD of approximately 0.31 μm. For this reason, also an exposure dose of 140 μC/cm2 could be used to arrive at an actual CD of 0.30 μm if the nominal CD was in turn shrank to approximately 0.29 μm. Therefore, an actual CD of 0.30 μm could either be realized by writing a 0.30 μm line width using an exposure dose of 120 μC/cm2 (i.e., the dose-to-size) or by writing a 0.29 μm line width using an exposure dose of 140 μC/cm2. Both process points in terms of an exposure dose of 120 μC/cm2 and an exposure dose of 140 μC/cm2 are equally valid for realizing an actual CD of 0.30 μm (assuming an appropriate size adaptation of the written pattern for the higher exposure dose).
There may be various considerations that favor one dose over the other to arrive at a target resist pattern (e.g., in terms of a target CD). For example, in many lithography processes the so-called isofocal dose will be the optimum process dose (in terms of the base dose set at the exposure apparatus). Originally, the isofocal process point has mainly been investigated in regard of optical lithography. It has recently been suggested to use the isofocal process point also for beam lithography processes, see Chris Mack, Electron-beam lithography simulation for mask making, part IV, proceedings of Photomask and X-Ray Mask Technology VI, SPIE Vol. 3748, pp. 27-40, and K. Keil et al, Determination of best focus and optimum dose for variable shaped e-beam systems by applying the isofocal dose method, Microelectronic Engineering 85 (2008) 778-781.
The isofocal dose is the process dose for which the actual CD is independent from the beam focus, as schematically illustrated in FIG. 3. The relevance of the isofocal dose derives from the fact that during the beam writing process, the beam is scanned or otherwise moved within the lithography field to write a pattern into the resist. The pattern-defining beam typically is at its best focus at the center of the lithography field and gets increasingly out of focus as it is directed to the borders of the lithography field, resulting in a larger spot size. In addition, resist thickness variations and an uneven substrate likewise contribute to the beam being out of focus. The influence of all these, and other, effects on the beam writing process can significantly be reduced when the exposure dose is set to the isofocal dose.
In practice, however, most beam writing apparatuses do not permit an intentional adjustment of the beam focus during the exposure process, or from one exposure process to the next. As such, the isofocal dose cannot easily be determined by experiments because the beam focus cannot actively be varied in an effort to derive the isofocal dose.
A further challenge in the experimental determination of the isofocal dose is the fact that the experimental data for dose calibration are correlated with many other process-dependent parameters that give rise to the so-called process bias. As this process bias-dependency cannot be easily decoupled in the experimental data from the base dose-dependency, there is presently no feasible way to properly calibrate the isofocal dose (or any other optimum process dose).
Prior art is known from US 2008/067446 A1 as well as US 2006/206851 A1.